Robust Numerical Method for Singularly Perturbed Parabolic Differential Equations with Negative Shifts

Abstract

This paper deals with singularly perturbed parabolic differential difference equations with delay on the first and zeroth order derivative terms. The solution of the onsidered problem exhibits boundary layer behaviour as the perturbation parameter tends to zero. The problem is solved using θ-method in temporal discretization and exponentially fitted finite difference method in spatial discretization. The convergence analysis and solution bound for stability is proved. The parameter uniform convergence analysis is carried out and is shown to be accurate of order O(N⁻² + (∆t)² ) for the case θ = 1/ 2 .